This book offers a comprehensive introduction to the theory of linear and nonlinear Volterra
integral equations (VIEs), ranging from Volterra's fundamental contributions and the …

In this article we describe recent progress on the design, analysis and implementation of
hybrid numerical-asymptotic boundary integral methods for boundary value problems for the …

We present some results on the complexity of numerical integration. We start with the
seminal paper of Bakhvalov (1959) and end with new results on the curse of dimensionality …

Trefftz methods are finite element-type schemes whose test and trial functions are (locally)
solutions of the targeted differential equation. They are particularly popular for time …

Fourier feature approximations have been successfully applied in the literature for scalable
Gaussian Process (GP) regression. In particular, Quadrature Fourier Features (QFF) derived …

Numerical integration is encountered in all fields of numerical analysis and the engineering
sciences. By now, various efficient and accurate quadrature rules are known, for instance …

This paper presents\textsc {hankel}, a pure-python code for solving Hankel-type integrals
and transforms. Such transforms are common in the physical sciences, especially appearing …

This thesis is concerned with the numerical treatment of hyperbolic conservation laws.
These play an important role in describing many natural phenomena. Challenges in their …

We present an O (N\rm log\, N) algorithm for the calculation of the first N coefficients in an
expansion of an analytic function in Legendre polynomials. In essence, the algorithm …

In this paper, new Levin methods are presented for calculating oscillatory integrals with
algebraic and/or logarithmic singularities. To avoid singularity, the technique of singularity …